Mathematical Problems In Linear Viscoelasticity
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Mathematical Problems In Linear Viscoelasticity
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Author : Mauro Fabrizio
language : en
Publisher: SIAM
Release Date : 1992-01-01
Mathematical Problems In Linear Viscoelasticity written by Mauro Fabrizio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Science categories.
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
Mathematical Problems In Linear Viscoelasticity
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Author : Mauro Fabrizio
language : en
Publisher: SIAM
Release Date : 1992-01-01
Mathematical Problems In Linear Viscoelasticity written by Mauro Fabrizio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Science categories.
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
Boundary Value Problems In Linear Viscoelasticity
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Author : John M. Golden
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Boundary Value Problems In Linear Viscoelasticity written by John M. Golden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).
Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition
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Author : Francesco Mainardi
language : en
Publisher: World Scientific
Release Date : 2022-08-16
Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition written by Francesco Mainardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-16 with Mathematics categories.
Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
Crack And Contact Problems For Viscoelastic Bodies
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Author : G.A.C. Graham
language : en
Publisher: Springer
Release Date : 2014-05-04
Crack And Contact Problems For Viscoelastic Bodies written by G.A.C. Graham and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Technology & Engineering categories.
The main emphasis of these Lecture Notes is on constructing solutions to specific viscoelastic boundary value problems; however properties of the equations of viscoelasticity that provide the theoretical underpinnings for constructing such solutions are also covered. Particular attention is paid to the solution of crack and contact problems. This work is of interest in the context of polymer fracture, modelling of material behaviour, rebound testing of polymers and the phenomenon of hysteretic friction.
Applications Of Viscoelasticity
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Author : Pouria Hajikarimi
language : en
Publisher: Elsevier
Release Date : 2021-04-27
Applications Of Viscoelasticity written by Pouria Hajikarimi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-27 with Technology & Engineering categories.
Applications of Viscoelasticity: Bituminous Materials Characterization and Modeling starts with an introduction to the theory of viscoelasticity, emphasizing its importance to various applications in material characterization and modeling. It next looks at constitutive viscoelastic functions, outlines basic equations for different loading conditions, and introduces the Boltzmann superposition principle, relaxation modulus, and creep compliance. Mechanical models, including integer-order and fractional-order are studied next, featuring real experimentation data alongside the benefits and drawbacks of using each model in various real-world scenarios. The book then covers the correspondence principle, followed by time–temperature superposition, featuring a simple procedure to construct a real master curve and challenges that might be encountered. The concluding chapters cover the Hopkins and Hamming, Park and Kim, and General Power law methods for interconversion of constitutive viscoelastic functions, applications of viscoelasticity for experimental tests, and incremental form of viscoelastic relations for numerical modeling. The book also includes supplementary codes that users can duplicate and use in their own work. - Takes an applied approach to material viscoelasticity, explaining complicated viscoelastic equations and principles - Presents examples of those equations and principles being applied to common problems in realworld settings - Covers constitutive viscoelastic functions, including relaxation modulus and creep compliance - Outlines the construction of a master curve of viscoelastic material considering time–temperature superposition - Couples the correspondence principle with common viscoelastic experiments, such as threepoint bending beam, axial and torsional bar, and dynamic shear rheometer - Provides supplementary codes
Seismic Waves In Laterally Inhomogeneous Media
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Author : Ivan Psencik
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Seismic Waves In Laterally Inhomogeneous Media written by Ivan Psencik and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
This special issue contains contributions presented at the international workshop Seismic Waves in Laterally Inhomogeneous Media V, which was held at the Castle of Zahrádky, Czech Republic, June 5 - 9, 2000. The workshop, which was attended by about 60 seismologists from 16 countries, was devoted mainly to the current state of theoretical and computational means of study of seismic wave propagation in complex structures. The special issue begins with papers dealing with the study and the application of the ray methods. Problems such as coupling of quasi-shear waves or smoothing of models for effective ray computations are dealt with. Applications of the ray methods in seismic exploration are presented. Further, directional wavefield decomposition, phase space, path integral and parabolic equation methods are discussed. Attention is also devoted to attenuation and scattering problems, and to seismic inversion problems.
Thermodynamics And Kinetic Theory Proceedings Of The 5th Bilateral Polish Italian Meeting
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Author : W Kosinski
language : en
Publisher: World Scientific
Release Date : 1992-03-27
Thermodynamics And Kinetic Theory Proceedings Of The 5th Bilateral Polish Italian Meeting written by W Kosinski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-27 with categories.
This book gives a comprehensive review of the current status of the theory of the pion-two-nucleon systems at intermediate energies. It also makes an extensive comparison of the theoretical prediction with the corresponding data obtained recently from the major meson factories.
Mathematical Models And Methods For Smart Materials
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Author : Mauro Fabrizio
language : en
Publisher: World Scientific
Release Date : 2002
Mathematical Models And Methods For Smart Materials written by Mauro Fabrizio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book contains the papers presented at the conference on "Mathematical Models and Methods for Smart Materials, " held in Italy in 2001. The papers are divided into four parts: "Methods in Materials Science" deals mainly with mathematical techniques fo the investigation of physical systems, such as liquid crystals, materials with internal variables, amorphous materials, and thermoelastic materials. Also, techniques are exhibited for the analysis of stability and controllability of classical models of continuum mechanics and of dynamical systems. "Modelling of Smart Materials" is devoted to models of superfluids, superconductors, materials with memory, nonlinear elastic solids, and damaged materials. In the elaboration of the models, thermodynamic aspects play a central role in the characterization of the constitutive properties. "Well-Posedness in Materials with Memory" deals with existence, uniqueness and stability for the solution of problems, most often expressed by integrodifferential equations, which involve materials with fading memory. Also, attention is given to exponential decay in viscoelasticity, inverse problems in heat conduction with memory, and automatic control for parabolic equations. "Analytic Problems in Phase Transitions" discusses nonlinear partial differential equations associated with phase transitions, and hysteresis, possibly involving fading memory effects. Particular applications are developed for the phase-field model with memory, the Stefan problem with a Cattaneo type equation, the hysteresis in thermo-visco plasticity, and the solid-solid phase transition. Contents: Automatic Control Problems for Integrodifferential Parabolic Equations (C Cavaterra);Phase Relaxation Problems with Memory and Their Optimal Control (P Colli); Unified Dynamics of Particles and Photons (G Ferrarese); Solid-Solid Phase Transition in a Mechanical System (G Gilardi); KAM Methods for Nonautonomous
Acoustic Interactions With Submerged Elastic Structures
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Author : Ardshir Guran
language : en
Publisher: World Scientific
Release Date : 2002
Acoustic Interactions With Submerged Elastic Structures written by Ardshir Guran and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This series of volumes constitutes an outstanding collection of contributions by the most active research workers in the area of acoustics and mechanics. It brings the reader up to date on the status of the various aspects of research in this field. The volumes should preserve their value for a long time, as they represent a monument to the achievements of human research capabilities in the underwater-acoustics aspects of the environment.